This present work is devoted to the investigation of the transient phenomena for a fiber-reinforced medium with a cylindrical cavity in the context of the three-phase-lag model of generalized thermoelasticity with a new form of derivative of the Caputo–Fabrizio (CF) type in the heat transport equation, where the medium is under the action of an induced magnetic field. The Laplace transform is incorporated as a tool for the solution of the problem when the boundary of the cavity is exposed to harmonically varying heat with a constant angular frequency of thermal vibration. The numerical inversion of the Laplace transforms is computed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of reinforcement, the angular frequencies on thermal vibrations, CF fractional parameter and magnetic field.